may have dropped a valve seat, I have replaced a motor in one that "makes noise" "runs poorly" leakdown on 2 cylinders were 40% and 70% dissasembly of the motor I found the 70% was a dropped exhaust valve seat... this wk had 65k miles on it but inside accessing the head bolts my deep socket was burried in sludge getting the lower head bolts, Timing chains and sliders severly worn (slack in bank 1 secondary chain), so I highly suggested a motor over repairing her sludged up worn out mess for nearly the same cost.
Its hard to say without having access to decent diagnostic tools... if your battery has been disconnected, make sure to drive it, accelerate then let off (X5 or 10 times). the adaptive numerator is lost with a battery disconnect and must be set for it to see misfires. From there you will hopefully see which cylinder is misifiring with a p030X code. If not your just going to have to look at all cylinders.
If I dont have a misfire code I pull all the plugs, look for any signs of damage or wear (probably not your issue considering the inciting incident). Compression tests are nice and cheap kits can be obtained but dont really tell you much, you really want a leakdown tester, FYI I used a harbor freight one in the past and it functioned as required and only required like 35psi... others can run 100psi. This will tell you where it is leaking. If you are able to do a leakdown test, make sure to take your radiator cap off, if its a head gasket concern you may do further cooling system damage pressurizing it to 35-100psi
. A leakdown will point you in the direction of what in the combustion chamber is failed.
Furthermore and a cheaper option (which may be inconclusive) you can get a "block test kit" from any parts store. It is simply a beaker that seals on your radiator fill neck and you fill it with a blue/purple chemical that turns yellow in the presence of hydrocarbons. Start the vehicle and let it run for a bit. One issue is the recent coolant flush. I cannot remember where maybe the instructions with the block tester, but its suggested to have some miles on the coolant to allow hydrocarbon-coolant comingling.
Ultimately with an overheat its likely not going to be a simple easy fix... IT MIGHT... but not likely, as mentioned, cast iron and aluminum cause issues with severe heat and metal expansion and contraction.